Question

x+2y=3,3x-2y=-7 find the value of x and y

Answer 1

$\large\underline{\sf{Solution-}}$

Given pair of equations are

$\red{\rm :\longmapsto\:x + 2y = 3}$

and

$\red{\rm :\longmapsto\:3x - 2y = - 7}$

On adding both the equations, we get

$\red{\rm :\longmapsto\:x + 2y + 3x - 2y = 3- 7}$

$\red{\rm :\longmapsto\:4x = - 4}$

$\red{\rm :\longmapsto\:x = - 1}$

On substituting x = - 1, in equation (1), we get

$\red{\rm :\longmapsto\: - 1+ 2y = 3}$

$\red{\rm :\longmapsto\: 2y = 3 + 1}$

$\red{\rm :\longmapsto\: 2y = 4}$

$\red{\rm :\longmapsto\: y = 2}$

So,

$\begin{gathered}\begin{gathered}\rm :\longmapsto\:\bf\: Solution \: is \: -\begin{cases} &\sf{x \: = - \: 1} \\ &\sf{y \: = \: 2} \end{cases}\end{gathered}\end{gathered}$

Verification :-

Consider equation,

$\purple{\rm :\longmapsto\:x + 2y = 3}$

On substituting x = - 1 and y = 2, we get

$\purple{\rm :\longmapsto\: - 1+ 2(2) = 3}$

$\purple{\rm :\longmapsto\: - 1+ 4 = 3}$

$\purple{\rm :\longmapsto\: 3 = 3}$

Hence, Verified

Now, Consider second equation,

$\blue{\rm :\longmapsto\:3x - 2y = - 7}$

On substituting the values of x and y, we get

$\blue{\rm :\longmapsto\:3( - 1) - 2(2) = - 7}$

$\blue{\rm :\longmapsto\: - 3 -4 = - 7}$

$\blue{\rm :\longmapsto\: - 7 = - 7}$

Hence, Verified

Answer 2

Question :-

x+2y=3,3x-2y=-7 find the value of x and y

Solution :-

Given equation :

• x + 2y = 3
• 3x - 2y = - 7

Need to find :

• x and y

Add both equation

$\sf:\longmapsto{x + 2y + 3x - 2y = 3 - 7} \\ \\ \sf:\longmapsto{4x = - 4} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bf:\longmapsto \red{x = - 1} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

Substitute x = -1 in equation (1)

$\sf:\longmapsto{ - 1 + 2y = 3} \\ \\ \sf:\longmapsto{2y = 3 + 1} \: \: \: \\ \\ \sf:\longmapsto{y = 2 } \: \: \: \: \: \: \: \: \: \: \:$

${\boxed{\rm{Verification : }}}$

Put values of x and y in eqⁿ (1)

$\sf: \longmapsto{ - 1 + 2(2) = 3} \\ \\ \sf: \longmapsto{ - 1 + 4 = 3} \: \: \: \: \: \\ \\ \bf: \longmapsto \red{3 = 3} \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

Hence Verified !

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